Question

When 1.960 g of titanium is combusted in a bomb calorimeter, the temperature of the calorimeter increases from 25.00 °C to 86.98 °C. In a separate experiment, the heat capacity of the calorimeter is measured to be 9.84 kJ/K. The heat of reaction for the combustion of a mole of Ti in this calorimeter is ________ kJ/mol.

Answer 1

To calculate the heat of reaction for titanium's combustion, multiply the heat capacity of the calorimeter by the temperature increase to find the total heat absorbed. Then, convert the mass of titanium to moles and divide the total heat by the number of moles to find the heat of reaction per mole, which is approximately 14880.42 kJ/mol.

Step-by-step explanation:

To find the heat of reaction for titanium's combustion, we use the formula Δq = C×ΔT, where Δq is the heat absorbed by the calorimeter (in kJ), C is its heat capacity (9.84 kJ/K), and ΔT is the change in temperature (86.98 °C - 25.00 °C).

Δq = 9.84 kJ/K × (86.98 °C - 25.00 °C) = 609.60 kJ

This is the amount of heat absorbed for the combustion of 1.960 g of titanium. To get the heat of reaction per mole, we convert grams to moles using titanium's molar mass (47.87 g/mol) and then divide the total heat absorbed by the number of moles.

Moles of Ti = 1.960 g / 47.87 g/mol = 0.04095 mol

Heat of reaction per mole = 609.60 kJ / 0.04095 mol = 14880.42 kJ/mol

The heat of reaction for the combustion of a mole of Ti in this calorimeter is approximately 14880.42 kJ/mol.

Answer 2

Answer : The heat of combustion of one mole of Ti is -14897.4 kJ/mole

Explanation :

First we have to calculate the heat gained by the calorimeter.

`q=c* (T_(final)-T_(initial))`

where,

q = heat gained by calorimeter = ?

c = specific heat =
`9.84kJ/K`

`T_(final)` = final temperature =
`25.00^oC=273+25.00=298.00K`

`T_(initial)` = initial temperature =
`86.98^oC=273+86.98=359.98K`

Now put all the given values in the above formula, we get:

`q=9.84kJ/K* (359.98-298.00)K`

`q=609.9kJ`

Heat released by the reaction = - Heat gained by calorimeter = -609.9 kJ

Now we have to calculate the heat of combustion of one mole of Ti.

To calculate the number of moles of Ti:

Molar mass of Ti = 47.87 g/mole

Number of moles Ti =
`\frac{\text{Mass of Ti}}{\text{Molar mass of Ti}}=(1.960g)/(47.87g/mol)=0.04094mole`

Heat of combustion of one mole of Ti =
`-(609.9kJ)/(0.04094mole)=-14897.4kJ/mole`

Therefore, the heat of combustion of one mole of Ti is -14897.4 kJ/mole